Ekeland Variational Principle in the Variable Exponent Sequence Spaces ℓp(·)
Abstract
:1. Introduction
2. Preliminaries
- (i)
- if, and only if, ;
- (ii)
- , if ;
- (iii)
- For arbitrary and any , the inequalityholds.
- (a)
- A sequence is υ-convergent to if, and only if, . Note that the υ-limit is unique if it exists.
- (b)
- A sequence is υ-Cauchy if as .
- (c)
- A subset is υ-closed if for any sequence that υ-converges to x, it holds .
3. Main Results
- (i)
- , for any ;
- (ii)
- ;
- (iii)
- and for any , we have
- (1)
- , for any ;
- (2)
- , for any .
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Abbreviations
MDPI | Multidisciplinary Digital Publishing Institute |
DOAJ | Directory of open access journals |
TLA | Three letter acronym |
LD | linear dichroism |
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Alfuraidan, M.R.; Khamsi, M.A. Ekeland Variational Principle in the Variable Exponent Sequence Spaces ℓp(·). Mathematics 2020, 8, 375. https://doi.org/10.3390/math8030375
Alfuraidan MR, Khamsi MA. Ekeland Variational Principle in the Variable Exponent Sequence Spaces ℓp(·). Mathematics. 2020; 8(3):375. https://doi.org/10.3390/math8030375
Chicago/Turabian StyleAlfuraidan, Monther R., and Mohamed A. Khamsi. 2020. "Ekeland Variational Principle in the Variable Exponent Sequence Spaces ℓp(·)" Mathematics 8, no. 3: 375. https://doi.org/10.3390/math8030375
APA StyleAlfuraidan, M. R., & Khamsi, M. A. (2020). Ekeland Variational Principle in the Variable Exponent Sequence Spaces ℓp(·). Mathematics, 8(3), 375. https://doi.org/10.3390/math8030375